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Opam

Electronics

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Opam

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  1. CIRCUITS AND ELECTRONICS 6.002 The Operational Amplifier Abstraction Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.002 Fall 2000 Lecture 19

  2. Review ? MOSFET amplifier — 3 ports + power port V + O v S output port + Iv input port – – – ? Amplifier abstraction V S + O v Iv + – + – Iv v – O Function of vI Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.002 Fall 2000 Lecture 19

  3. Review O v Iv Function of vI ? Can use as an abstract building block for more complex circuits (of course, need to be careful about input and output). ? Today Introduce a more powerful amplifier abstraction and use it to build more complex circuits. Reading: Chapter 15 from A & L. Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.002 Fall 2000 Lecture 19

  4. Operational Amplifier Op Amp V S power port +– + input port output port – +– S V − More abstract representation: + + v OUT v IN – – Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.002 Fall 2000 Lecture 19

  5. Circuit model (ideal): O v i+ = 0 v+ + v + – Av v– – → ∞ A i– = 0 i.e. ? ∞ input resistance ? 0 output resistance ? “A” virtually ∞ ? No saturation Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.002 Fall 2000 Lecture 19

  6. Using it… +– = 12V VS V 12 O v + v IN – R − = − VS V 12 L – 12V + Demo active region O v 12 V saturation v IN − 10 μV 10 μV 6 A ~ 10 but unreliable, temp. dependent − 12 V (Note: possible confusion with MOSFET saturation!) Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.002 Fall 2000 Lecture 19

  7. Let us build a circuit… Circuit: noninverting amplifier v + + O v − v +– – v 1 R IN R 2 Equivalent circuit model op amp i+ = 0 + O v v ( ) + – +−v − A v +– v 1 R IN − v i– = 0 R 2 Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.002 Fall 2000 Lecture 19

  8. Let us analyze the circuit: Find vOin terms of vIN, etc. ( ) +− − = vO A v v ⎛ ⎞ R = − ⎜ ⎝ ⎟ ⎠ A v v 2 IN O + R R 1 2 ⎞ ⎛ AR + = + ⎟ ⎠ ⎜ ⎝ v 1 Av 2 R O IN R 1 2 Av = v IN AR + O + 1 2 R R 1 2 What happens when “A” is very large? Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.002 Fall 2000 Lecture 19

  9. Let’s see… When A is large Av v + Av ≈ = IN IN AR + AR + O 2 R 1 2 R R R 1 2 1 2 ( ) + R R ≈ v 1 2 IN R 2 Suppose A = R1= R = 2 10 = 6 10 9 R ⋅ gain R 6 v v IN O 6 10 R + 1 + 9 R ⋅ R 6 10 v = Demo IN ⋅ 1 + 6 1 10 10 ≈ ⋅ v v 10 O IN Gain: ? determined by resistor ratio ? insensitive to A, temperature, fab variations Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.002 Fall 2000 Lecture 19

  10. Why did this happen? Insight: 5V + v 12V 10V + v = 2 v A − v O IN 5V +– – v R vO IN 6V 6V – i = 2 0 negative feedback R e.g. vIN= 5V Suppose I perturb the circuit… (e.g., force vOmomentarily to 12V somehow). Stable point is when v+ ≈ v-. Key: negative feedback ? portion of output fed to –ve input. e.g. Car antilock brakes ? small corrections. Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.002 Fall 2000 Lecture 19

  11. Question: How to control a high-strung device? Antilock brakes is it turning? yes/no feedback it’s all about control Mic helin no yes apply release disc v. v. powerful brakes Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.002 Fall 2000 Lecture 19

  12. More op amp insights: Observe, under negative feedback, ⎞ ⎛ + R R ⎟ ⎠ ⎜ ⎝ v 1 2 IN R v + − → − = = 1 0 v v O A A +≈ v − v We also know i+ ≈ 0 i -≈ 0 ?yields an easier analysis method (under negative feedback). Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.002 Fall 2000 Lecture 19

  13. Insightful analysis method under negative feedback + − ≈ v v + ≈ i 0 − ≈ i 0 + R R g = v v 1 2 a v O IN R IN 2 + O v v b +– IN – v v 1 R f IN IN c v R IN 2 e = i 0 v d IN R 2 R 2 Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.002 Fall 2000 Lecture 19

  14. Question: a v + v IN c + v ? IN O v − v +– – b v v IN IN v ≈ v O IN + R R or = v v 1 2 O IN R 2 with 1= R R 0 ∞ = 2 Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.002 Fall 2000 Lecture 19

  15. Why is this circuit useful? + O v +– – v IN v ≈ v O IN Buffer voltage gain = 1 input impedance = ∞ output impedance = 0 current gain = ∞ power gain = ∞ Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.002 Fall 2000 Lecture 19

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